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import sympy as sy
import numpy as np
from sympy.functions import sin,cos
import matplotlib.pyplot as plt
from sympy import E
plt.style.use("ggplot")
# Define the variable and the function to approximate
x = sy.Symbol('x')
f = sin(x)
# Factorial function
def factorial(n):
if n <= 0:
return 1
else:
return n*factorial(n-1)
# Taylor approximation at x0 of the function 'function'
# Since I'm still having difficulting getting this to work, I can just create individual functions for each equation (since I don't need the whole thing).
#Make sure you create a function estimating the upper bound error
def taylor(function,x0,n,a):
i = 0
p = 0
while i <= n:
p = p + (function.diff(x,i).subs(x,x0))/(factorial(i))*(x-x0)**i
i += 1
# u = (M / factorial(n + 1)) * (x - x0)**(n+1)
return p
e = E.evalf()
print(taylor(e**x,0.5,5,1))
print("Break")
print(taylor(e**x, 0.05,5,0.1))
print("Break")
print(taylor(e**x,0.005,5,0.01))
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